Following Trinh and Ramkrishna (1996a, Chem. Engng Sci., in press), spatial patterns due to steady-state multiplicity in catalyst particles in a packed-bed catalytic reactor is investigated further under isothermal conditions. In this work, axial dispersion is included in the fluid phase while the assumption of lumped resistance to transport (within the particles) at the particle surface is retained. A region is identified in the relevant parameter space in which spatial patterns are assured to exist. Conditions are established for asymptotic stability as well as stability in a specially defined 'topology' due to Weinberger (1982, Lecture Notes in Numer. Appl. Anal., Vol. 5, p. 354). This topology signifies how much the prevailing profile in the reactor may vary from a specific steady-state pattern. It is used to specify the initial perturbation of the reactor from the pattern in order that the reactor output stays within some stipulated range of product quality thus allowing the reactor to remain within a particular class of patterns.